QUESTION IMAGE
Question
expressions-polynomials-evaluate add subtract polynomials: p
(1 point)
determine the following for: \\( 3x^3 - 5x^2 + x - 9 \\)
a) determine the coefficient and the degree of each term.
| term | coefficient | degree |
|---|---|---|
| \\( -5x^2 \\) | \\( \square \\) | \\( \square \\) |
| \\( x \\) | \\( \square \\) | \\( \square \\) |
| \\( -9 \\) | \\( \square \\) | \\( \square \\) |
b) the degree of the polynomial is \\( \square \\),
the leading term is \\( \square \\),
and the leading coefficient is \\( \square \\).
Part (a)
Term \( 3x^3 \)
Step1: Find Coefficient
The coefficient is the numerical factor, so for \( 3x^3 \), coefficient is \( 3 \).
Step2: Find Degree
Degree is the exponent of \( x \), so degree is \( 3 \).
Term \( -5x^2 \)
Step1: Find Coefficient
Numerical factor is \( -5 \), so coefficient is \( -5 \).
Step2: Find Degree
Exponent of \( x \) is \( 2 \), so degree is \( 2 \).
Term \( x \) (which is \( 1x^1 \))
Step1: Find Coefficient
Numerical factor is \( 1 \), so coefficient is \( 1 \).
Step2: Find Degree
Exponent of \( x \) is \( 1 \), so degree is \( 1 \).
Term \( -9 \) (which is \( -9x^0 \))
Step1: Find Coefficient
Numerical factor is \( -9 \), so coefficient is \( -9 \).
Step2: Find Degree
Exponent of \( x \) (implicit \( x^0 \)) is \( 0 \), so degree is \( 0 \).
Part (b)
Degree of Polynomial
The degree of a polynomial is the highest degree of its terms. From part (a), the highest degree is \( 3 \).
Leading Term
Leading term is the term with the highest degree, which is \( 3x^3 \).
Leading Coefficient
Leading coefficient is the coefficient of the leading term, which is \( 3 \).
Filling the Table for Part (a)
| Term | Coefficient | Degree |
|---|---|---|
| \( -5x^2 \) | \( -5 \) | \( 2 \) |
| \( x \) | \( 1 \) | \( 1 \) |
| \( -9 \) | \( -9 \) | \( 0 \) |
Final Answers for Part (b)
- Degree of polynomial: \( 3 \)
- Leading term: \( 3x^3 \)
- Leading coefficient: \( 3 \)
Summary of Answers
Part (a) Table:
As filled above.
Part (b):
- Degree: \( \boldsymbol{3} \)
- Leading Term: \( \boldsymbol{3x^3} \)
- Leading Coefficient: \( \boldsymbol{3} \)
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Part (a)
Term \( 3x^3 \)
Step1: Find Coefficient
The coefficient is the numerical factor, so for \( 3x^3 \), coefficient is \( 3 \).
Step2: Find Degree
Degree is the exponent of \( x \), so degree is \( 3 \).
Term \( -5x^2 \)
Step1: Find Coefficient
Numerical factor is \( -5 \), so coefficient is \( -5 \).
Step2: Find Degree
Exponent of \( x \) is \( 2 \), so degree is \( 2 \).
Term \( x \) (which is \( 1x^1 \))
Step1: Find Coefficient
Numerical factor is \( 1 \), so coefficient is \( 1 \).
Step2: Find Degree
Exponent of \( x \) is \( 1 \), so degree is \( 1 \).
Term \( -9 \) (which is \( -9x^0 \))
Step1: Find Coefficient
Numerical factor is \( -9 \), so coefficient is \( -9 \).
Step2: Find Degree
Exponent of \( x \) (implicit \( x^0 \)) is \( 0 \), so degree is \( 0 \).
Part (b)
Degree of Polynomial
The degree of a polynomial is the highest degree of its terms. From part (a), the highest degree is \( 3 \).
Leading Term
Leading term is the term with the highest degree, which is \( 3x^3 \).
Leading Coefficient
Leading coefficient is the coefficient of the leading term, which is \( 3 \).
Filling the Table for Part (a)
| Term | Coefficient | Degree |
|---|---|---|
| \( -5x^2 \) | \( -5 \) | \( 2 \) |
| \( x \) | \( 1 \) | \( 1 \) |
| \( -9 \) | \( -9 \) | \( 0 \) |
Final Answers for Part (b)
- Degree of polynomial: \( 3 \)
- Leading term: \( 3x^3 \)
- Leading coefficient: \( 3 \)
Summary of Answers
Part (a) Table:
As filled above.
Part (b):
- Degree: \( \boldsymbol{3} \)
- Leading Term: \( \boldsymbol{3x^3} \)
- Leading Coefficient: \( \boldsymbol{3} \)